%change in X- Inflation- Elasticity

GDP/Inflation

• Inflation rate is measured by using a price index for two years. The consumer price index may give a value of goods for year X1 and another value for year X2.

The equation is: (Index for X2 – Index for X1) / Index for X1 x 100

• Example problem: Average index for year X1 is 104 and average index for year X2 is 108

The inflation rate is (108 – 104) / 104 x 100 = 3.85%

However, this calculation is very simplistic. Categories within the CPI are weighted, and this has to be taken account of in calculation for inflation.

Inflation rate = 141.3 – 133 / 133 x 100 = 6.24%

Category

Index for

year X1

Weight

Index for X1 times weight

Index for

year X2

Weight

Index for X2 times weight

Housing 140 0.5 70 150 0.5 75

Foodstuff

132 0.3 39.6 141 0.3 42.3

Clothing

117 0.2 23.4 120 0.2 24

Totals 1.0 133 1.0 141.3

Definitions

• GDP: The monetary value of the aggregate output of an economy

• Nominal GDP: The GDP of a country in current prices or market value of a nation’s output

• Real GDP: GDP that has been adjusted for inflation to a base-year price

• Inflation: A persistent increase in the average price level in the economy

• Consumer Price Index (CPI): A weighted price index of goods and services typically purchased by urban consumers.

Definition

• Price Elasticity of Demand (PED): Measures how much quantity demanded of a product changes when there is a change in the price of a product.

• Cross Elasticity of Demand(XED): Measures how much the demand for a product changes when there is a change in the price of another product.

• Income Elasticity of Demand (YED): Measures of how much the demand for a product changes when there is a change in the consumer’s income.

• Price Elasticity of Supply (PES): Measures how much the supply of a product changes when there is a change in the price of a product.

How to calculate

• PED= Percentage Change in Quantity Demanded/ Percentage change in Price

• PES= Percentage Change in Quantity Supplied/ Percentage Change in Price

• XED= Percentage Change in quantity of Product X/ Percentage Change in price of Product Y

• YED= Percentage change in quantity demanded of product/ Percentage change in income of consumer

Elasticity Equations

• Percentage Change in Quantity Demanded = (Qd2-Qd1/Qd1) *100

• Percentage Change in Price of Product= (P2-P1/P1)*100

• Percentage Change in Consumer Income = (I2-I1/I1)*100

• Percentage Change in Quantity Supplied= (Qs2-Qs1/Qs1)*100

Question

• PED Question: When a firm discovers that when they lower the price of one of their monthly magazines from $5-$4.5, the number of magazines that are bought by customers each month rises form 200,000 to 230,000. Calculate the PED.

Answer• Calculate percentage change in quantity demanded

((230,000-200,000)/200,000)*100

(30,000/200,000)*100

= 15%

• Calculate percentage change in Price.

((4.50-5.00)/5.00) *100

(-.5/5.00)*100

= -10%

PED= 15% / -10% = -1.5 

Ignore negative value

PED is 1.5, so it is Elastic.

Question

• XED Question: Price of Burger lowers from, $2.0 to $1.8. As a result, the number of pizza slices that a different shop owner falls from 400 to 380.

• Find the XED for the pizza slices.

Answer

• Calculate percentage change in quantity demanded

((400-380)/400)*100

(-20/400)*100

= -5%

• Calculate percentage change in Price of Y

((2-1.8)/2) *100

(-.2/2)*100

= -10%

XED= -5% / -10% = 0.5

Because XED is positive, two goods are substitutes of each other.

Question

• YED Question: Person’s annual income increase from $60,000 per year to $66,000 per year. Person increases annual spending on holidays from $2,500 to $3,000. Find her income elasticity of demand for holidays.

Answer• Percentage change in Quantity demanded of holidays

((3,000-2,500)/2,500)*100

(500/2,500)*100

= 20%

• Calculate percentage change in income

((66,000-60,000)/60,000)*100

(6,000/60,000)*100

= 10%

YED= 20% / 10 % = 2

Positive value, so good is a normal good. Value is also above 1, so the good is demand is income-elastic.

Question

• PES Question: Magazine prices change from $5.00 to $5.50. The magazine firm’s supply increases fro, 200,000 to 230,000 magazines per month. Calculate PES.

Answer

• Calculate percentage change in quantity supplied

((230,000-200,000)/200,000)*100

(30,000/200,000)*100

= 15%

• Calculate percentage change in price.

((5.5-5.0)/5.0)*100

(.5/5.0)*100

= 10%

PES= 15% / 10% = 1.5

• PES is positive and above 1, so supply is elastic.